Question: Simplify; express your answer in exponential form. Assume $y\neq 0, t\neq 0$. $\dfrac{{(y^{-1}t^{-5})^{5}}}{{(y^{2}t^{3})^{-2}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(y^{-1}t^{-5})^{5} = (y^{-1})^{5}(t^{-5})^{5}}$ On the left, we have ${y^{-1}}$ to the exponent ${5}$ . Now ${-1 \times 5 = -5}$ , so ${(y^{-1})^{5} = y^{-5}}$ Apply the ideas above to simplify the equation. $\dfrac{{(y^{-1}t^{-5})^{5}}}{{(y^{2}t^{3})^{-2}}} = \dfrac{{y^{-5}t^{-25}}}{{y^{-4}t^{-6}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{-5}t^{-25}}}{{y^{-4}t^{-6}}} = \dfrac{{y^{-5}}}{{y^{-4}}} \cdot \dfrac{{t^{-25}}}{{t^{-6}}} = y^{{-5} - {(-4)}} \cdot t^{{-25} - {(-6)}} = y^{-1}t^{-19}$